The calculational advantages of the Wigner-Wilkins thermal flux spectra make it a desirable theory to use for the determination of thermal group constants in water-moderated reactor systems; however, the physical assumptions required by the theory are far from satisfied by water, and an experimental verification of the theory is called for. Such data have been furnished by M. J. Poole at Harwell. Comparisons with calculations from the theory of Wigner and Wilkins show surprisingly good agreement, although some consistent deviations are noted.